Optimal age replacement policies with multiple missions for multi-state systems

The mission duration plays a very vital role in maintaining engineering systems in reality. This paper considers the mission duration into the age replacement policies with multiple missions for multi-state systems (MSSs). We first introduce the MSS whose degradation process follows a non-homogenous continuous time Markov process. Then, the basic replacement policy is given, and the optimum number of missions is derived analytically and numerically. To address the trade-off between the cost and maintainability, we consider the replacement time in maintenance and propose two policies, i.e., replacement first and replacement last. The optimal policies of each replacement are discussed analytically. Numerical examples are proposed to verify the applicability of the methodology derived by this paper. Finally, the suggested replacement policies are illustrated in maintaining the coal transportation system in a power station based on the assumed data.